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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 8550.bl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8550.bl1 | 8550t2 | \([1, -1, 1, -121880, -16189253]\) | \(651038076963/7220000\) | \(2220488437500000\) | \([2]\) | \(92160\) | \(1.7590\) | |
8550.bl2 | 8550t1 | \([1, -1, 1, -13880, 226747]\) | \(961504803/486400\) | \(149590800000000\) | \([2]\) | \(46080\) | \(1.4125\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.bl have rank \(0\).
Complex multiplication
The elliptic curves in class 8550.bl do not have complex multiplication.Modular form 8550.2.a.bl
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.